一类具有合作与自限效应的 Extended Fisher-Kolmogorov 系统的定态分歧

Abstract

Abstract:

This paper investigates the steady-state bifurcation to a class of Extended Fisher-Kolmogorov system with cooperative and self-limiting effects. By using the extended Lyapunov-Schmidt reduction method and the spectral decomposition theorem for linear completely continuous fields, the bifurcation of the system under Dirichlet boundary conditions are analyzed. Explicit expressions for the bifurcating solutions are provided, and the regularity of these solutions are discussed, revealing that biological populations exhibit periodic fluctuations. Under Neumann boundary conditions, complete criteria for supercritical and subcritical bifurcations are obtained, and the regularity of the bifurcating solution is explored. When the system undergoes a supercritical bifurcation, the population size gradually expands; when it undergoes a subcritical bifurcation, the population size initially plummets before gradually stabilizing.

Key words: Extended Fisher-Kolmogorov system, Dirichlet boundary, Neumann boundary, steady-state bifurcation, Lyapunov-Schmidt reduction, regularity

CLC Number:

O175.29

Chao Zhu, Qingming Hao, Zhigang Pan, Yanhua Wang. Steady-State Bifurcation to a Class of Extended Fisher-Kolmogorov System with Cooperative and Self-Limiting Effects[J].Acta mathematica scientia,Series A, 2025, 45(5): 1432-1443.

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Steady-State Bifurcation to a Class of Extended Fisher-Kolmogorov System with Cooperative and Self-Limiting Effects

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